Sacred Geometry and the Platonic Solids
by Liliana Usvat
The term "sacred geometry" is used by archaeologists, anthropologists, and geometricians to encompass the religious, philosohical, and spiritual beliefs that have sprung up around geometry in various cultures during the course of human history.
Sacred geometry involves sacred universal patterns used in the design of everything in our reality, most often seen in sacred architecture and sacred art. The basic belief is that geometry and mathematical ratios, harmonics and proportion are also found in music, light, cosmology. This value system is seen as widespread even in prehistory, a cultural universal of the human condition.
At the very earliest appearance of human civilization we observe the presence and importance of geometry. It is clearly evident that geometry was comprehended and utilized by the ancient Master Builders, who, laboring at the dawn of civilization some four and one half millennia ago, bestowed upon the world such masterworks as the megalithic structures of ancient Europe, the Pyramids and temples of Pharaonic Egypt and the stepped Ziggurats of Sumeria. That geometry continued to be employed throughout the centuries from those earliest times until times historically recent is also clearly evident.
Ancinet Artifacts The Platonic Solids.
Some researchers have suggested that carved stone balls were attempts to realise the Platonic solids. There are five (and only five) Platonic solids (regular polyhedra). These are: - the tetrahedron (4 faces), cube (6 faces), octahedron (8 faces), dodecahedron (12 faces) and icosahedron (20 faces). They get their name from the ancient Greek philosopher and mathematician Plato (c427-347BC) who wrote about them in his treatise, Timaeus. ( Was he the first that wrote about them or we lost ancinet information and knowledges?)
Hundreds of carved stone spheres, roughly three inches in diameter, believed to date to around 2000 BC, have been found in Scotland. Some are carved with lines corresponding to the edges of regular polyhedra. Roughly half have 6 knobs---like the one at right above---but the others range from three to 160 knobs. The more mathematically regular ones do not appear to have had a special importance. For example, in addition to the 12-knob dodecahedral form shown in the center and just to its right above, there are also ones with 14 knobs, corresponding to a form with two opposite hexagons, each surrounded by six pentagons. Nonetheless, the dodecahedron appears here long before the Greeks wrote of it. The function of these stones is unknown and so it is unclear whether I should list them here under the category art, but many are intricately carved with spirals or cross-hatching on the faces. The material varies from easily carved sandstone and serpentine to difficult, hard granite and quartzite.
Greeks about Platonic Solids
The Greeks taught that these five solids were the core patterns of physical creation. Four of the solids were seen as the archetypal patterns behind the four elements (earth, air, fire, and water), while the fifth was held to be the pattern behind the life force itself, the Greeks' ether. These shapes predominated in the hundreds of carved prehistoric petrospheres found in Scotland with over 75% representing one of the Platonic Solids. They came from a time over a thousand years earlier than the Greeks. These same shapes are now realised to be intimately related to the arrangements of protons and neutrons in the elements of the periodic table.
The theory of the 'Harmony of the Spheres' proposed by Plato who died around 347BC follower of Pythagoras and who shared his belief that the universe’s secrets lay maths and its numbers., in which he envisioned the five 'perfect' solids to be enclosed within imaginary spheres, each placed within the other. He proposed that the distances of the planets from the sun showed similar ratios from each other as the spheres surrounding each solids did. Modern science has indeed shown that planets have unique 'vibrations', or 'sounds' supporting Plato's conjecture.
"Because the Pythagoreans thought that the heavenly bodies were separated from one another by intervals corresponding to the harmonic lengths of strings, they held that the movement of the spheres gives rise to a musical sound called the "harmony of the spheres."
The Golden Ratio - The Divine Scale
The golden ratio describes the special relationship found in nature between two parts of a whole. It can be described in terms of number, length, area, volume and, to a certain degree, beauty and consciousness.
We are a microcosmic reflection of the macrocosm. The structure of the human body is based upon the same set of principles that are found functioning on all levels of creation. Our body contains within it holographically all the information of the universe.
Initiation into understanding
• The Universe is made of one substance and has one shape – the Sine Wave.
• The world is made up of waves and sacred proportions.
• Geometry produces symmetry. Waves get permission to arrange themselves and to store memory from ‘ONENESS’, through the Golden Mean ‘Phi’ ratio – the secret of the universe and the most accurate scientific pure principle to describe how things relate and function, evolve, change and manifest.
• Waves are drawn to FOCUS and automatically sort themselves and agree to sustain via Sacred Geometry. They align to still points, creating ‘CHARGE’, ‘ecstasy’ and LIFE FORCE.
• When the harmonics of the brain-body-heart-planet enter into NESTING, they do so by the principal of FRACTALITY. The small is within the large; the pattern of your fingertip is the same as the galaxy.
• The doorway of perception is to holographically connect all of life processes – past, present and future.
History
The ancient cultures (Celts, Druids, Egyptians, Knights Templar, etc...) and aboriginal peoples (Mayan, Hopi, etc...) were very much aware of these geometrical signatures and numeric frequencies.
Five Platonic Solids
The first of the platonic solids is the tetrahedron having 4 triangular sides and symbolizing the element of fire.
Tetrahedron
The first of the platonic solids is the tetrahedron having 4 triangular sides and symbolizing the element of fire.
Meaning: the power of fire and the power present in the tetrahedron are beneficial for creating change but need to be handled with utmost care.
Cube or Hexahedron
The second platonic solid is the cube or hexahedron having 6 square sides and representing the element of earth.
Meaning: a solid foundation and stability suggesting a need for patience and consistency, allowing things to develop in their own perfect time.
Octahedron
The third of the platonic solids in the octahedron having 8 triangular sides and symbolizing the element of air.
Meaning: careful balance between multiple forces suggesting the need for diplomacy, grace and willingness to learn.
Dodecahedron
The fourth platonic solid is the Dodecahedron symbol for the universes and having 12 pentagonal sides.
Meaning: a framework for the descending subtle energies of spirit. This suggests a time in which the divine forces must lead the way whether the understanding is there or not.
Icosahedron
The Icosahedron is the fifth and final platonic solid having 20 triangular sides and symbol for the element of water.
Meaning: trust in the wisdom of the universe is needed with a willingness to allow others to assist in the situation versus pursuing an active role. As the water suggests, it time to go with the flow.
Major Scientists artist of the world knew about Platonic solids. Leonardo da Vinci was one of them.
Leonardo da Vinci drew the illustrationsfor Luca Pacioli's 1509 book De Divina Proportione (The Divine Proportion)
Leonardo Da VInci was passioate in Mathematics. He drew other figures for the Luca Pacioli's book.
Leonardo da Vinci - Geometric Figure Duodecendron elevatus vacuus .
Leonardo da Vinci drew the illustrations for Luca Pacioli's 1509 book De Divina Proportione (The Divine Proportion). Drawing of the truncated icosahedron, from the manuscript of the book.
Here is another of Leonardo da Vinci Drawing for Luca Pacioli's 1509 book De Divina Proportione (The Divine Proportion) of the Duodecedron Abscisus Elevatus Vacuus, consisting of 120 equilateral triangles. (Stellations of The Platonic Solids and The Archimedean Solids)
Dimensionality
The progression from point (0-dimensional) to line (1-dimensional) to plane (2-dimensional) to space (3-dimensional) and beyond leads us to the question – if mapping from higher order dimensions to lower ones loses vital information (as we can readily observe with optical illusions resulting from third to second dimensional mapping), does our “fixation” with a 3-dimensional space introduce crucial distortions in our view of reality that a higher-dimensional perspective would not lead us to?
More about Platonic Solids
The 5 Platonic solids (Tetrahedron, Cube or (Hexahedron), Octahedron, Dodecahedron and Icosahedron) are ideal, primal models of crystal patterns that occur throughout the world of minerals in countless variations. These are the only five regular polyhedra, that is, the only five solids made from the same equilateral, equiangular polygons. To the Greeks, these solids symbolized fire, earth, air, spirit (or ether) and water respectively. The cube and octahedron are duals, meaning that one can be created by connecting the midpoints of the faces of the other. The icosahedron and dodecahedron are also duals of each other, and three mutually perpendicular, mutually bisecting golden rectangles can be drawn connecting their vertices and midpoints, respectively. The tetrahedron is a dual to itself.
The Archimedean Solids
There are 13 Archimedean solids, each of which are composed of two or more different regular polygons. Interestingly, 5 (Platonic) and 13 (Archimedean) are both Fibonacci numbers, and 5, 12 and 13 form a perfect right triangle.
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